In this work, we have systematically studied the structural, energetic and electronic properties of graphene functionalized with carbene groups by using density functional theory. Introducing a low concentration of CCl2 group in graphene was studied in detail by DFT, and closed cyclopropane-like three-membered ring structure was formed, meanwhile, the potential candidate carbene groups CR2 (R = H, F, CH3, CN, NO2, OCH3, CCH, C6H5) were added to graphene sheet, and CR2 (R = H, NO2, CH3) groups were expected to be good reactive species to covalently modify graphene. The graphene functionalization with carbene groups above can open graphene's band gap. More CCl2 molecules were added to graphene, and different concentrations of CCl2 group can tune graphene's band gap. In addition, the addition of CCl2 group to graphene edges was investigated, and the stronger binding energy was found. Multiple CCl2 molecules preferred to be bound with the same edge of graphene nanoribbon. This work provides an insight into the detailed molecular mechanism of graphene functionalization with carbene groups. (C) 2014 Elsevier B.V. All rights reserved.